math hl ia ideas

Mathematics HL Internal Assessment Student Checklist Student Name: _____ Date: _____ 1. 31) Graham’s Number – a number so big that thinking about it could literally collapse your brain into a black hole. 31) The Shoelace Algorithm to find areas of polygons. Ideas for Math HL IA? You can download these here. It shouldn't look like copy - paste from an article or Wikipedia. IB math HL IA/ Exploration ideas Watch. Some nice examples of using polar coordinates to create interesting designs. A good example of how to conduct a statistical investigation in mathematics. 1) The prisoner’s dilemma: The use of game theory in psychology and economics. Quiz 3. If you’ve never come across this site before, start by exploring the IB Maths SL/HL/Studies Videos tab at the top of the website. IB DP Mathematics SL: Home Topic 1: Algebra Topic 2: Functions and Equations Topic 3: Circular Functions and Trigonometry Topic 4: Vectors Topic 5: Statistics and Probability Topic 6: Calculus External Assessment Internal Assessment Math SL outline: File Size: 118 kb: File Type: docx: Download File. Zeno’s paradox of Achilles and the tortoise, The Poincare Conjecture and Grigori Perelman, The Monkey and the Hunter – How to Shoot a Monkey, Galileo: Throwing cannonballs off The Leaning Tower of Pisa. Yoga. IB Revision Notes for Analysis and Applications. Really useful! How to use modeling to predict booms and busts. 37) Modelling a Nuclear War. 12) How to win at Rock Paper Scissors. 40) Stellar Numbers – This is an excellent example of a pattern  sequence investigation. 28) Ford Circles– how to generate Ford circles and their links with fractions. 1) Modular arithmetic – This technique is used throughout Number Theory. 6) Impact Earth – what would happen if an asteroid or meteorite hit the Earth? IB Physics 100 Concepts+tips. Full length rough draft submitted prior to winter break for review. Please note that difference between HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently the HL and SL grades differ slightly. Go to first unread Skip to page: This discussion is closed. 36) Can we prove that 1 + 2 + 3 + 4 …. 68 Mathematics HL guide Internal assessment Internal assessment criteria The exploration is internally assessed by the teacher and externally moderated by the IB using assessment criteria that relate to the objectives for mathematics HL. Still feeling confused? The challenge is to see how many different shapes can be made with a given number of squares – and how can they fit together? Here is a list of 20 interesting topics to help you get inspiration: 1. 3) Galileo: Throwing cannonballs off The Leaning Tower of Pisa – Recreating Galileo’s classic experiment, and using maths to understand the surprising result. Close. 16) Graphing polygons investigation. New II: Paper 3 Practice Questions for HL. Quantum Mechanics – a statistical universe? Investigate how binary is used – link to codes and computing. 6) Square Triangular Numbers. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL). 41) Arithmetic number puzzle – It could be interesting to do an exploration where you solve number problems – like this one. Check out this article! Can we find a function that plots a square? A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. Massive library of useful links and videos. Pre-Diploma Quizzes Show sub menu. 23) Perfect Numbers: Perfect numbers are the sum of their factors (apart from the last factor). ( Log Out /  Can you find the pattern behind it? 14) Methods for solving differential equations – Differential equations are amazingly powerful at modelling real life – from population growth to to pendulum motion. I’ve teamed up with Mr Mac to provide full class revision notes fully updated for the new syllabus. The following are examples of HL/SL IAs based on the current mark scheme with grader comments. Maths Exploration (IA) ideas. 11) Flatland by Edwin Abbott – This famous book helps understand how to imagine extra dimension. Complex Numbers. 16) Euler’s identity: An equation that has been voted the most beautiful equation of all time, Euler’s identity links together 5 of the most important numbers in mathematics. … 30) Maths of Global Warming – Modeling Climate Change – Using Desmos to model the change in atmospheric Carbon Dioxide. 11) Zeno’s paradox of Achilles and the tortoise: How can a running Achilles ever catch the tortoise if in the time taken to halve the distance, the tortoise has moved yet further away? How to use graphic software to make art from equations. Breaking the Code Euler’s Totient Theorem Minesweeper… IB Exploration Modelling and Statistics Guide. ibalasia. 6) Handshake problem: With n people in a room, how many handshakes are required so that everyone shakes hands with everyone else? 18) Hyperbolic geometry – how we can map the infinite hyperbolic plane onto the unit circle, and how this inspired the art of Escher. But no matter what the topic is about and whether you are super good and interested in math or not, you can get at least a mark 6/7, if you follow certain guidelines, including but not limited to perfect presentation, clear formulae, exact structure, logical development of the ideas, personal approach to the work(i.e. Are there functions which plot any polygons? Can you solve Oxford University’s Interview Question? 3) Benford’s Law – using statistics to catch criminals by making use of a surprising distribution. Use the binomial distribution to test your ESP abilities. 19) Elliptical Curves– how this class of curves have importance in solving Fermat’s Last Theorem and in cryptography. This is a fantastic 70 page booklet explaining different modelling methods from Moody’s Mega Maths Challenge. 23) Modelling music with sine waves – how we can understand different notes by sine waves of different frequencies. 300 IB Maths Exploration ideas, video tutorials and Exploration Guides, September 3, 2013 in IB Maths, Real life maths, ToK maths | Tags: british international school phuket, internal investigation, maths exploration, maths IA. 1) The Monkey and the Hunter – How to Shoot a Monkey – Using Newtonian mathematics to  decide where to aim when shooting a monkey in a tree. Find out! 1) Traffic flow: How maths can model traffic on the roads. Applications of differentiation. 15) Julia Sets and Mandelbrot Sets – We can use complex numbers to create beautiful patterns of infinitely repeating fractals. Includes: Thanks for the list, was very useful for me (currently choosing a topic for the math exploration). A nice starting point for students good at coding – who want to put these skills to the test mathematically. 6) Mandelbrot set and fractal shapes: Explore the world of infinitely generated pictures and fractional dimensions. 9) Designing bridges – Mathematics is essential for engineers such as bridge builders – investigate how to design structures that carry weight without collapse. Regardless, the IA is all about EXPLORATION. The formula given to us was: =∫ 2 Hence, I wondered if there was a similar way in which the surface area of a solid of revolution could be found through calculus. 2. 1b) The shape of the universe – non-Euclidean Geometry is at the heart of Einstein’s theories on General Relativity and essential to understanding the shape and behavior of the universe. A post which looks at the maths behind this particularly troublesome series. Premier League wages and league position? Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. The Shoelace Algorithm to find areas of polygons. 27) Could Trump win the next election? 11) Understanding the fourth dimension: How we can use mathematics to imagine (and test for) extra dimensions. Bivariate Statistics. but these range from quite easy (modular arithmetic, at least at the basic level) to impossibly hard (GRH? Essential knowledge for future astronauts. 19) Introduction to Modelling. Beautifully written by an experienced IB Mathematics teacher, and of an exceptionally high quality. Bivariate Statistics. Still feeling confused? Instructions for January 22 and January 25: you are going to research the Internal Assessment for this class, called the Math Exploration. How do you even choose a topic? During Maths HL class, we were taught how to utilise integral calculus in order to find the volume of a solid of revolution in the interval [ , ]. This Math Class included two current UC Berkeley Students, an Oxford pupil, and a UPenn undergrad. Here are some examples solved using Python. Fourier transforms have an essential part to play in modern life – and are one of the keys to understanding the world around us. For example, Mod 3 means the remainder when dividing by 3. You can also model everything from Angry Birds to stunt bike jumping. All rights reserved. 6) Continued fractions: These are fractions which continue to infinity. 7) Explore the Si(x) function – a special function in calculus that can’t be integrated into an elementary function. The formula given to us was: =∫ 2 Hence, I wondered if there was a similar way in which the surface area of a … There has been a recent breakthrough in this problem. Maths Books. This particular problem was solved by Euler. During Maths HL class, we were taught how to utilise integral calculus in order to find the volume of a solid of revolution in the interval [ , ]. Mathematics HL Internal Assessment Student Checklist Student Name: _____ Date: _____ 1. 18) Which times tables do students find most difficult? 5) Knight’s tour in chess: This chess puzzle asks how many moves a knight must make to visit all squares on a chess board. 28) How to avoid a Troll – an example of a problem solving based investigation, 29) The Gini Coefficient – How to model economic inequality. 25) Palindrome numbers: Palindrome numbers are the same backwards as forwards. Pros: IB specific. The Practice Exams section takes you to ready made exams on each topic – again with worked solutions. 2) Logistic function and constrained growth 3) Benford's Law - using statistics to catch criminals by making use of a surprising distribution. Find out how! Pascal’s triangle patterns: Fibonacci sequence. 4) Why e is base of natural logarithm function: A chance to investigate the amazing number e. 5) Fourier Transforms – the most important tool in mathematics? The only real thing that I came up with is something to do with statistics and Pokemon, but those don't seem to work well because all the probabilities are already preprogrammed in the game. However, there are definitely ways to improve on it. How strange things happen when we start to manipulate divergent series. This is a nice geometry puzzle solved using a variety of methods. Stacking cannonballs – solving maths with code, Project Euler: Coding to Solve Maths Problems, Hollow Cubes and Hypercubes investigation, Methods for solving differential equations, Finding the average distance between 2 points on a hypercube, Find the average distance between 2 points on a square, Generating e through probability and hypercubes, IB HL Paper 3 Practice Questions Exam Pack, Complex Numbers as Matrices: Euler’s Identity, Sierpinski Triangle: A picture of infinity, The Tusi couple – A circle rolling inside a circle, Further investigation of the Mordell Equation, Rational Approximations to Irrational Numbers – A 78 Year old Conjecture Proved, IB Applications and Interpretations SL and HL Resources, IB Analysis and Approaches SL and HL Resources, The Gini Coefficient – measuring inequality, Follow IB Maths Resources from British International School Phuket on WordPress.com. Maths is closely connected with astronomy – see how we can work out the distance to the stars. Any ideas for some not-so-generic Math IA topics? 2) Hexaflexagons: These are origami style shapes that through folding can reveal extra faces. Advice on using Geogebra, Desmos and Tracker. 11) The Monty Hall problem – this video will show why statistics often lead you to unintuitive results. 7) Black Swan events – how usefully can mathematics predict small probability high impact events? Straight lines are not straight, parallel lines meet and angles in a triangle don’t add up to 180 degrees. 27) Volume optimization of a cuboid  – how to use calculus and graphical solutions to optimize the volume of a cuboid. Quiz 4. 13) Different number systems – Learn how to add, subtract, multiply and divide in Binary. You can watch a short video on it here. This topic links to graph theory. Can we prove that 1 + 2 + 3 + 4 …. Together this is around 120 pages of content. Quiz 1. 3) Gambler’s fallacy: A good chance to investigate misconceptions in probability and probabilities in gambling. The use of regression in polling predictions. 14) Circular inversion – what does it mean to reflect in a circle? 12) Magic squares and cubes: Investigate magic tricks that use mathematics. Projectile!motion–!Mathematics!IA!!! Using the physics of travel near the speed of light to see how we could travel to other stars. Announcements Help shape TSR for a chance to win a £100 voucher >> Applying to uni? What is the minimum number of colours needed for any map? Choosing the topic is usually the trickiest part which many IB students struggle with. Writers Per Hours is a renowned writing service with an excellent track record in IB HL and SL standards. Over 300 examples of maths IA exploration topics and ideas for IB mathematics. 35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory. There’s a really great website been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams. Introduction! More computing led investigations. – An essential component of JPEG, DNA analysis, WIFI signals, MRI scans, guitar amps – find out about the maths behind these essential technologies. 46) Ramanujan’s Taxi Cab and the Sum of 2 Cubes. Also look at the finances behind Premier league teams. Arthur was literally the ONLY person in his HL Math Class that got a 7 on his Math IA. 36) Predicting the UK election using linear regression. 17) Medical data mining – Explore the use and misuse of statistics in medicine and science. Quiz 5. 2) How to Design a Parachute – looking at the physics behind parachute design to ensure a safe landing! How many people need to be in a room for it to be at least 50% likely that two people will share the same birthday? The final mark for each exploration is the sum I'm completely lost and can't think of any ideas. For Parents. 1) Radiocarbon dating – understanding radioactive decay allows scientists and historians to accurately work out something’s age – whether it be from thousands or even millions of years ago. 5) Königsberg bridge problem: The use of networks to solve problems. 45) The Mordell Equation. Which times tables do students find most difficult? 28. There is also a fully typed up mark scheme. Please like, comment and subscribe for more videos! Useful websites for use in the exploration, A selection of detailed exploration ideas. We can use a Poisson model and some Excel expertise to predict the outcome of sports matches – a technique used by gambling firms. I would really recommend these resources for all IB students – it takes a lot of skill to successfully condense a syllabus into the essential content – and these notes really are of the highest quality. 17) Chinese remainder theorem. Most of these are excellent and I love the majority (CRT is the Way, the Truth, and the Light!) 10) Is there a correlation between Premier League wages and league position? ... Maths Exploration (IA) ideas. 40) Modelling the spread of Coronavirus (COVID-19). How all our digital communications are kept safe through the properties of primes. If you are watching this video now, you seem serious about boosting your IB grade. It involves understanding the modulo operation. What topic I should choose? 17) Graphing Stewie from Family Guy. Stuck for Ideas planning your Biology IA? IB HL Math IA Topics (Mathematics in art~expolring the role of math in…: IB HL Math IA Topics 5) Stacking cannon balls: An investigation into the patterns formed from stacking canon balls in different ways. Quiz 2. Copyright 2020 Lanterna Education ltd, not affiliated with the IBO. I'd recommend a modelling exploration, though, if I really have license to recommend anything. A great introduction to some of the ideas behind non-euclidean geometry. 33) The Chinese Remainder Theorem: This is a method developed by a Chinese mathematician Sun Zi over 1500 years ago to solve a numerical puzzle. 35) Fun with Functions!. Change ). Investigate what changes the condition of numbers, So there we have it, 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! Together this is around 120 pages of content. 7) Quantum Mechanics – a statistical universe? I have chosen math hl and economics hl as well. The following are examples of HL/SL IAs based on the current mark scheme with grader comments. Continuous random variables. https://www.lanternaeducation.com/ib-blog/50-ib-maths-ia-topic-ideas Posted by. 38) Friendly numbers, Solitary numbers, perfect numbers. HL Mathematics IA (18/20) Maths IA For the IA, I encourage you to start as soon as possible – the more time you spend on it, the more you think about the maths you’re putting into it and hence, there will be a lower chance of you making mistakes that will cost you marks. Remember! Fully updated for the new syllabus. Choose your own pattern investigation for the exploration. Really helpful, I had no idea on even where to start. The planets follow a surprising pattern when measuring their distances. 26) Modelling volcanoes – look at how the Poisson distribution can predict volcanic eruptions, and perhaps explore some more advanced statistical tests. What’s the difference between IB Literature vs. IB Language & Literature. 16) Are we living in a computer simulation? 32) Circular Motion: Modelling a Ferris wheel. You can download these notes on my site here. 10) Mathematical card tricks – investigate some maths magic. 2) Torus – solid of revolution: A torus is a donut shape which introduces some interesting topological ideas. Go to  this website to find examples of the Math Exploration Click on a specific paper and you will find three options: 1) the paper, 2) … 4) Tesseract – a 4D cube: How we can use maths to imagine higher dimensions. 13) Graphically understanding complex roots – have you ever wondered what the complex root of a quadratic actually means graphically? Some classic physics – which generates some nice mathematical graphs. Fermat’s Last Theorem is one of the most famous such equations. Is your IA written entirely by yourself, and trying to avoid simply replicating work and ideas from sources you found during research? Qualified Writers in: Math, Biology, Physics, ESS, History, Economics, Chemistry, Geography, Music, Computer Science or even Design and Technology! IB Maths Resources from British International School Phuket, I’ve teamed up with Mr Mac to provide full class revision notes fully updated for the new syllabus. Listen to the sounds that different sine waves make. 37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur. An interesting insight into the mathematical field of Number Theory. Investigate how to solve them. ... Maths Exploration (IA) ideas. There are many types of HL Math IA: 1. If you are asking, “what is a good topic for a Math IA”, we can help you brainstorm. What is the geometric shape of soap bubbles? [2020 Updated] IB Maths HL Key Exam Concepts & Practice Exam Questions! IBDP Math HL Show sub menu. If you could send me a copy a copy of you Math hl IA, it would be of great help. Completely Free. 4) Bluffing in Poker: How probability and game theory can be used to explore the the best strategies for bluffing in poker. 5 and 7 are consecutive primes). Please note that difference between HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently the HL and SL grades differ slightly. 16) Hyperbolic functions – These are linked to the normal trigonometric functions but with notable differences. I’ve just put together seventeen full investigation questions – each one designed to last around 1 hour, and totaling around 40 pages and 600 marks worth of content. 2/3 could be written as 1/6 + 1/2. Is Bitcoin going to keep rising or crash? In some geometries triangles add up to more than 180 degrees, in others less than 180 degrees. Circular measure. Breaking the Code Euler’s Totient Theorem Minesweeper… Also, what is with “Does finger length predict mathematical ability?”? Where do you even begin such a task? Within each topic listed below, we include the basic reasons for investigating each topic, what the possible independent variables and dependent variables are as well as the basic experimental setup! Fourier Transforms – the most important tool in mathematics? Binomial Theorem. 2. There is a $1 million prize for solving the Riemann Hypothesis and $250,000 available for anyone who discovers a new, really big prime number. Choosing a good topic is tricky. How the normal distribution is used to predict elections. All fully updated for the new syllabus. 10) Is Intergalactic space travel possible? I would really recommend these resources for all IB students – it takes a lot of skill to successfully condense a syllabus into the essential content – and these notes really are of the highest quality. The IB wants to see you take an idea, explore what is interesting about it, and show how engaged you are with the topic. Complex Numbers. Look at the inherent probabilistic nature of the universe with some quantum mechanics. 2. 44) Modelling Chaos – how we can use grahical software to understand the behavior of sequences. 2) Goldbach’s conjecture: “Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics. This is a nice way to link some maths history with studying an interesting function. 14) Bayes’ theorem: How understanding probability is essential to our legal system. Why e is base of natural logarithm function: Fourier Transforms – the most important tool in mathematics? 30) Can you solve Oxford University’s Interview Question?. You choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources: The Questionbank takes you to a breakdown of each main subject area (e.g. Aaryan is one of our many tutors who smashed their Maths IA. Includes: Full revision notes for SL Analysis (60 pages), HL Analysis (112 pages) and SL Applications (53 pages). Hey everyone. 5) Fourier Transforms – the most important tool in mathematics? 43) Narcissistic Numbers – what makes a number narcissistic – and how can we find them all? 7) Sierpinksi triangle: a fractal design that continues forever. This mathematical equation has been described as the most important in all of physics. It’s quite funny how (almost) everyone doing the IB would have the thought process of the following when finding a topic for their Math IA: 1. Based on my experience, a topic solely focusing on a single geometric problem will not earn good scores. 25) Euler’s 9 Point Circle. Algebra, Calculus etc) and each area then has a number of graded questions. 20) The Coastline Paradox – how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions. These are beautifully  handwritten and of a very high quality. Quiz 1. 32) RSA code – the most important code in the world? 15) Birthday paradox: The birthday paradox shows how intuitive ideas on probability can often be wrong.

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